Best wall to deaden sound

Resilient channel can be very effective, IF installed properly (not difficult but there is definitely a right way and several wrong ways). Do some Internet searching on installation techniques. Here are a couple of links to get started.

You will also want to learn about 'acoustic sealant' and the various types of expanding foams available in aerosol cans for sealing ALL joints, cracks, utility perforations, etc. Connecting doors must be weatherstripped, sill seal must be effective. Read up also about how to deal with 'flanking noise'. You have received some suggestions about how to decouple the floor slab, should it prove necessary (you may want to get on-site professional advice here to avoid cutting utilities or compromising structural integrity). Similar concerns may also pertain to vibrations transmitted from the shop ceiling and exterior walls through their structural connections to the house.

David Merrill

mounting for the wall.

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There aren't a whole lot of continuous loud high-frequency metal shop sounds, just the occasional angle grinder and shop vac. Not like a wood shop.

Anyway it takes only another inch to make a staggerred double wall. Fir out the top and bottom plates an inch, then build another 2x4 wall with studs at the halfway spacing an inch out from the existing drywall, and hang the new drywall from that.

Anyway if you need to hang stuff on the wall, make a plywood sandwich. Sheath the wall with plywood or OSB, then drywall over that.